Problem: Simplify the following expression: $\dfrac{88a}{132a}$ You can assume $a \neq 0$.
Explanation: $ \dfrac{88a}{132a} = \dfrac{88}{132} \cdot \dfrac{a}{a} $ To simplify $\frac{88}{132}$ , find the greatest common factor (GCD) of $88$ and $132$ $88 = 2 \cdot 2 \cdot 2 \cdot 11$ $132 = 2 \cdot 2 \cdot 3 \cdot 11$ $ \mbox{GCD}(88, 132) = 2 \cdot 2 \cdot 11 = 44 $ $ \dfrac{88}{132} \cdot \dfrac{a}{a} = \dfrac{44 \cdot 2}{44 \cdot 3} \cdot \dfrac{a}{a} $ $\phantom{ \dfrac{88}{132} \cdot \dfrac{1}{1}} = \dfrac{2}{3} \cdot \dfrac{a}{a} $ $ \dfrac{a}{a} = 1 $ $ \dfrac{2}{3} \cdot 1 = \dfrac{2}{3} $